A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of R n. It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these " partial quotients " , so called determinants, are defined. It is pro...

It is known that for every nonorientable surface there are infinitely many (large) snarks that can be polyhedrally embedded on that surface. We take a dual approach to the embedding of snarks on the Klein bottle, and investigate edge-colorings of 6-chromatic triangulations of the Klein bottle. In the process, we discover the smallest snarks that can be polyhedrally embedded on the Klein bottle....

The standard Klein bottle coefficient in the construction of open descendants is shown to equal the Frobenius-Schur indicator of a conformal field theory. Other consistent Klein bottle projections are shown to correspond to simple currents. These observations enable us to generalize the standard open string construction from C-diagonal parent theories to include non-standard Klein bottles. Usin...

A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of R. It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these “partial quotients”, so called determinants, are defined. It is proved t...

Zusammenfassung Ein erheblicher Anteil der Parteimitglieder in Deutschland entfällt auf Klein(st)parteien. So stellt die Gruppe Klein(st)parteien summiert drittmeisten Deutschland. In Anbetracht einer wachsenden Anzahl und eines zunehmenden Stimmenanteils von ist steigenden Relevanz ihrer Mitgliedschaft auszugehen. Über diese große ist, trotz vieler Untersuchungen Parteimitgliedern im Allgemein...

Complex classical Cayley-Klein categories A(j), B(j), C(j) and D(j) are constructed by the method of categorical extension of the complex classical Cayley-Klein groups SL(2n; j;C), SO(2n + 1; j;C), Sp(2n; j;C) and SO(2n; j;C), respectively. The explicit construction of the irreducible representations of the complex classical Cayley-Klein categories is received. Completeness of lists of the irre...

In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...

We propose that cold dark matter is made of Kaluza-Klein particles and explore avenues for its detection. The lightest Kaluza-Klein state is an excellent dark matter candidate if standard model particles propagate in extra dimensions and Kaluza-Klein parity is conserved. We consider Kaluza-Klein gauge bosons. In sharp contrast to the case of supersymmetric dark matter, these annihilate to hard ...